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<td class="classHeaderTableLabel">Class</td><td class="classSignature">public class ALNutation</td>
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<p></p>
  Nutation(장동)
  <p></p>
<br>
<span class="label">Example</span>
<br>  <div class='listing'><pre>
  var JDE:Number = 2446895.5;
  var nutation:ALNutation = new ALNutation( JDE, ALNutation.HIGH_ACCURACY, ALNutation.LONG_PERIOD );
  trace( "JDE: " + nutation.JDE ); //JDE: 2446895.5
  trace( "accurcy: " + nutation.accuracy ); //accurcy: highAccuracy
  trace( "period: " + nutation.period ); //period: longPeriod
  trace( "Δψ : " + nutation.longitude ALConst.R2S); //Δψ : -3.787917163078442
  trace( "Δε : " + nutation.obliquity ALConst.R2S); //Δε : 9.442520698757397
  trace( "ε0 : " + ALDMS.fractionalDegree2DMS( nutation.meanObliquityOfEcliptic ALConst.R2D ).toString() ); //ε0 : 23° 26’ 27”.37
  trace( "ε  : " + ALDMS.fractionalDegree2DMS( nutation.trueObliquityOfEcliptic ALConst.R2D ).toString() ); //ε  : 23° 26’ 36”.81
  
  //JDE는 같지만 적용기간을 길게 잡는다. 이는 오랜 시간이 지나도 오차를 적게내도록 한다.
  nutation.accuracy = ALNutation.HIGH_ACCURACY;
  nutation.period = ALNutation.SHORT_PERIOD;
  trace( "JDE: " + nutation.JDE ); //JDE: 2446895.5
  trace( "accurcy: " + nutation.accuracy ); //accurcy: highAccuracy
  trace( "peroid: " + nutation.period ); //peroid: shortPeriod
  trace( "Δψ : " + nutation.longitude ALConst.R2S); //Δψ : -3.787917163078442
  trace( "Δε : " + nutation.obliquity ALConst.R2S); //Δε : 9.442520698757397
  trace( "ε0 : " + ALDMS.fractionalDegree2DMS( nutation.meanObliquityOfEcliptic ALConst.R2D ).toString() ); //ε0 : 23° 26’ 27”.41
  trace( "ε  : " + ALDMS.fractionalDegree2DMS( nutation.trueObliquityOfEcliptic ALConst.R2D ).toString() ); //ε  : 23° 26’ 36”.85
  
  //2028년 11월 13.19일 UT1
  var date:ALDate = new ALDate( 2028, 11, 13.19 );
  var deltaT:Number = ALDynamicalTime.deltaT( date.fractionalYear );
  JDE = date.JD + deltaT / 3600;
  nutation.JDE = date.JD;
  trace( "JDE: " + nutation.JDE ); //JDE: 2462088.689583333
  trace( "accurcy: " + nutation.accuracy ); //accurcy: highAccuracy
  trace( "peroid: " + nutation.period ); //peroid: shortPeriod
  trace( "Δψ : " + nutation.longitude ALConst.R2S); //Δψ : 14.860843903561848
  trace( "Δε : " + nutation.obliquity ALConst.R2S); //Δε : 2.7046046954480025
  trace( "ε0 : " + ALDMS.fractionalDegree2DMS( nutation.meanObliquityOfEcliptic ALConst.R2D ).toString() ); //ε0 : 23° 26’ 07”.93
  trace( "ε  : " + ALDMS.fractionalDegree2DMS( nutation.trueObliquityOfEcliptic ALConst.R2D ).toString() ); //ε  : 23° 26’ 10”.64 
  
  //Nutation이 적용된 Matrix를 받아와 별의 적경(2h24m11.331s=41°.5472),적위(+49°20'54".54=+49°.3485)에 적용 
  //Astronomical Algorithms 2nd p.153
  var equNutationMatrix:ALMatrix3D = nutation.getNutationOfEquMatrix();
  var equVector:ALVector3D = new ALVector3D( 41.5472 ALConst.D2R, 49.3485 ALConst.D2R, 1, ALVector3D.COORDINATE_TYPE_SPHERICAL );
  var equNutationVectorArray:Array = equNutationMatrix.multiply3x3ByVector3D( [equVector] );
  var equNutationVector:ALVector3D = equNutationVectorArray[0];
  trace( "RA : " + ALHMS.fractionalHour2HMS( equNutationVector.longitudeHour ).toString("h","m","s") ); //RA : 02h46m12.38s
  trace( "DE : " + ALDMS.fractionalDegree2DMS( equNutationVector.latitudeDegree ).toString() ); //DE : 49° 21’ 00”.82
  trace( "dRA : " + (equNutationVector.longitude - RA) ALConst.R2S ); //dRA : 15.843198038325333
  trace( "dDE : " + (equNutationVector.latitude - DE) ALConst.R2S ); //dDE : 6.217170560031128
   </pre></div>
  <p></p>
<p>
<span class="classHeaderTableLabel">See also</span>
</p>
<div class="seeAlso">
<a href="http://en.wikipedia.org/wiki/Nutation" target="mm_external">Astronomy on the personal computer 4th 6.4.2 Nutation page. 123 Astronomical Algorithms 2nd Chanpter 22 page.143</a>
</div>
<br>
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<a name="propertySummary"></a>
<div class="summarySection">
<div class="summaryTableTitle">Public Properties</div>
<table id="summaryTableProperty" class="summaryTable " cellpadding="3" cellspacing="0">
<tr>
<th>&nbsp;</th><th colspan="2">Property</th><th class="summaryTableOwnerCol">Defined&nbsp;by</th>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#accuracy">accuracy</a> : String<div class="summaryTableDescription">
   정확도.</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#JDE">JDE</a> : Number<div class="summaryTableDescription">
   Julian Ephemeris Date(JDE).</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#longitude">longitude</a> : Number<div class="summaryTableDescription">[read-only]
   Δψ : nutation in longitude(황도상에서 장동운동에 의한 황경 변화값)
   
   <p>
   High accuracy<br> 
     use 1980 IAU Theory of Nutation<br>
   Low accuracy : 0.5 arcsecond 정확도<br> 
     use Δψ = -17".20 sin Ω - 1".32 sin 2L - 0".23 sin 2L' + 0".21 sin 2Ω<br>
   </p>
   </div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#meanObliquityOfEcliptic">meanObliquityOfEcliptic</a> : Number<div class="summaryTableDescription">[read-only]
   ε0 : the mean obliquity of the ecliptic(적도와 황도의 기울기 평균값)<br>
   단위 radian
   
   </div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#obliquity">obliquity</a> : Number<div class="summaryTableDescription">[read-only]
   Δε : the nutation in obliquity(황도상에서 장동운동에 의한 기울기 변화값)
   
   <p>
   High accuracy<br> 
    use 1980 IAU Theory of Nutation <br>
   Low accuracy : 0.1 arcsecond 정확도<br> 
    use Δε = +9".20 cos Ω + 0".57 cos 2L + 0".10 cos 2L' - 0".09 cos 2Ω
   </p>
   </div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#period">period</a> : String<div class="summaryTableDescription">
   적용기잔.</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#trueObliquityOfEcliptic">trueObliquityOfEcliptic</a> : Number<div class="summaryTableDescription">[read-only]
   ε : the true obliquity of the ecliptic(적도와 황도의 기울기 실제값)<br> 
   ε = ε0 + Δε
   </div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
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<a name="methodSummary"></a>
<div class="summarySection">
<div class="summaryTableTitle">Public Methods</div>
<table id="summaryTableMethod" class="summaryTable " cellpadding="3" cellspacing="0">
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<th>&nbsp;</th><th colspan="2">Method</th><th class="summaryTableOwnerCol">Defined&nbsp;by</th>
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<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol">
<div class="summarySignature">
<a class="signatureLink" href="#ALNutation()">ALNutation</a>(JDE:Number, accuracy:String = "highAccuracy", period:String = "longPeriod")</div>
<div class="summaryTableDescription">
   장동운동 생성자
   </div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol">
<div class="summarySignature">
<a class="signatureLink" href="#getNutationOfEquMatrix()">getNutationOfEquMatrix</a>():<a href="../astro/ALMatrix3D.html">ALMatrix3D</a>
</div>
<div class="summaryTableDescription">
   Nutation of Equatorial Coordinate Transformation Matrix<br>
   nutation in longitude(Δψ)과 obliquity and obliquity(Δε)는 황도좌표계에서 계산된다.</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
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<a name="constantSummary"></a>
<div class="summarySection">
<div class="summaryTableTitle">Public Constants</div>
<table id="summaryTableConstant" class="summaryTable " cellpadding="3" cellspacing="0">
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<th>&nbsp;</th><th colspan="2">Constant</th><th class="summaryTableOwnerCol">Defined&nbsp;by</th>
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<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#HIGH_ACCURACY">HIGH_ACCURACY</a> : String = "highAccuracy"<div class="summaryTableDescription">[static]</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#LONG_PERIOD">LONG_PERIOD</a> : String = "longPeriod"<div class="summaryTableDescription">[static]</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#LOW_ACCURACY">LOW_ACCURACY</a> : String = "lowAccuracy"<div class="summaryTableDescription">[static]</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
</tr>
<tr class="">
<td class="summaryTablePaddingCol">&nbsp;</td><td class="summaryTableInheritanceCol">&nbsp;</td><td class="summaryTableSignatureCol"><a class="signatureLink" href="#SHORT_PERIOD">SHORT_PERIOD</a> : String = "shortPeriod"<div class="summaryTableDescription">[static]</div>
</td><td class="summaryTableOwnerCol">ALNutation</td>
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<a name="accuracy"></a>
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<td class="detailHeaderName">accuracy</td><td class="detailHeaderType">property</td>
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<code>accuracy:String</code>&nbsp;&nbsp;[read-write]<p>
   정확도. ALNutation.HIGH_ACCURACY 또는 ALNutation.LOW_ACCURACY 설정 
   </p><span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get accuracy():String</code>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function set accuracy(value:String):void</code>
<br>
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<a name="JDE"></a>
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<td class="detailHeaderName">JDE</td><td class="detailHeaderType">property</td><td class="detailHeaderRule">&nbsp;</td>
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<div class="detailBody">
<code>JDE:Number</code>&nbsp;&nbsp;[read-write]<p>
   Julian Ephemeris Date(JDE). JDE = JD + deltaT / 86400;
   </p><span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get JDE():Number</code>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function set JDE(value:Number):void</code>
<br>
</div>
<a name="longitude"></a>
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<td class="detailHeaderName">longitude</td><td class="detailHeaderType">property</td><td class="detailHeaderRule">&nbsp;</td>
</tr>
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<div class="detailBody">
<code>longitude:Number</code>&nbsp;&nbsp;[read-only]<p>
   Δψ : nutation in longitude(황도상에서 장동운동에 의한 황경 변화값)
   
   </p><p>
   High accuracy<br> 
     use 1980 IAU Theory of Nutation<br>
   Low accuracy : 0.5 arcsecond 정확도<br> 
     use Δψ = -17".20 sin Ω - 1".32 sin 2L - 0".23 sin 2L' + 0".21 sin 2Ω<br>
   </p>
   <span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get longitude():Number</code>
<br>
</div>
<a name="meanObliquityOfEcliptic"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">meanObliquityOfEcliptic</td><td class="detailHeaderType">property</td><td class="detailHeaderRule">&nbsp;</td>
</tr>
</table>
<div class="detailBody">
<code>meanObliquityOfEcliptic:Number</code>&nbsp;&nbsp;[read-only]<p>
   ε0 : the mean obliquity of the ecliptic(적도와 황도의 기울기 평균값)<br>
   단위 radian
   
   </p><span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get meanObliquityOfEcliptic():Number</code>
<br>
</div>
<a name="obliquity"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">obliquity</td><td class="detailHeaderType">property</td><td class="detailHeaderRule">&nbsp;</td>
</tr>
</table>
<div class="detailBody">
<code>obliquity:Number</code>&nbsp;&nbsp;[read-only]<p>
   Δε : the nutation in obliquity(황도상에서 장동운동에 의한 기울기 변화값)
   
   </p><p>
   High accuracy<br> 
    use 1980 IAU Theory of Nutation <br>
   Low accuracy : 0.1 arcsecond 정확도<br> 
    use Δε = +9".20 cos Ω + 0".57 cos 2L + 0".10 cos 2L' - 0".09 cos 2Ω
   </p>
   <span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get obliquity():Number</code>
<br>
</div>
<a name="period"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">period</td><td class="detailHeaderType">property</td><td class="detailHeaderRule">&nbsp;</td>
</tr>
</table>
<div class="detailBody">
<code>period:String</code>&nbsp;&nbsp;[read-write]<p>
   적용기잔. ALNutation.LONG_PERIOD 또는 ALNutation.SHORT_PERIOD 설정 
   </p><span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get period():String</code>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function set period(value:String):void</code>
<br>
</div>
<a name="trueObliquityOfEcliptic"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">trueObliquityOfEcliptic</td><td class="detailHeaderType">property</td><td class="detailHeaderRule">&nbsp;</td>
</tr>
</table>
<div class="detailBody">
<code>trueObliquityOfEcliptic:Number</code>&nbsp;&nbsp;[read-only]<p>
   ε : the true obliquity of the ecliptic(적도와 황도의 기울기 실제값)<br> 
   ε = ε0 + Δε
   </p><span class="label">Implementation</span>
<br>
<code>&nbsp;&nbsp;&nbsp;&nbsp;public function get trueObliquityOfEcliptic():Number</code>
<br>
</div>
<a name="constructorDetail"></a>
<div class="detailSectionHeader">Constructor detail</div>
<a name="ALNutation()"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">ALNutation</td><td class="detailHeaderParens">()</td><td class="detailHeaderType">constructor</td>
</tr>
</table>
<div class="detailBody">
<code>public function ALNutation(JDE:Number, accuracy:String = "highAccuracy", period:String = "longPeriod")</code><p>
   장동운동 생성자
   </p><span class="label">Parameters</span>
<table border="0" cellspacing="0" cellpadding="0">
<tr>
<td width="20px"></td><td><code><span class="label">JDE</span>:Number</code> &mdash; Julian Ephemeris Date(JDE). JDE = JD + deltaT / 86400
   </td>
</tr>
<tr>
<td class="paramSpacer">&nbsp;</td>
</tr>
<tr>
<td width="20px"></td><td><code><span class="label">accuracy</span>:String</code> (default = "<code>highAccuracy</code>")<code></code></td>
</tr>
<tr>
<td class="paramSpacer">&nbsp;</td>
</tr>
<tr>
<td width="20px"></td><td><code><span class="label">period</span>:String</code> (default = "<code>longPeriod</code>")<code></code></td>
</tr>
</table>
</div>
<a name="methodDetail"></a>
<div class="detailSectionHeader">Method detail</div>
<a name="getNutationOfEquMatrix()"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">getNutationOfEquMatrix</td><td class="detailHeaderParens">()</td><td class="detailHeaderType">method</td>
</tr>
</table>
<div class="detailBody">
<code>public function getNutationOfEquMatrix():<a href="../astro/ALMatrix3D.html">ALMatrix3D</a></code><p>
   Nutation of Equatorial Coordinate Transformation Matrix<br>
   nutation in longitude(Δψ)과 obliquity and obliquity(Δε)는 황도좌표계에서 계산된다.
   계산된 값은 적도좌표계로 변환하기 위한 행렬을 만들기 위해 쓰인다. 
   만들어진 행렬은 3번 회전한 건데 먼저 주어진 날짜로 X축 회전, Δψ를 적용한 Z축 회전, Δε를 적용한 x축 회전이다.
   
   </p><p></p>
<span class="label">Returns</span>
<table border="0" cellspacing="0" cellpadding="0">
<tr>
<td width="20"></td><td><code><a href="../astro/ALMatrix3D.html">ALMatrix3D</a></code></td>
</tr>
</table>
<p>
<span class="label">See also</span>
</p>
<div class="seeAlso">on the personal computer 4th p.123 Astronomical Algorithms 2nd p.151 Astronomical Almanic page B20</div>
</div>
<a name="constantDetail"></a>
<div class="detailSectionHeader">Constant detail</div>
<a name="HIGH_ACCURACY"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">HIGH_ACCURACY</td><td class="detailHeaderType">constant</td>
</tr>
</table>
<div class="detailBody">
<code>public static const HIGH_ACCURACY:String = "highAccuracy"</code>
</div>
<a name="LONG_PERIOD"></a>
<table cellspacing="0" cellpadding="0" class="detailHeader">
<tr>
<td class="detailHeaderName">LONG_PERIOD</td><td class="detailHeaderType">constant</td><td class="detailHeaderRule">&nbsp;</td>
</tr>
</table>
<div class="detailBody">
<code>public static const LONG_PERIOD:String = "longPeriod"</code>
</div>
<a name="LOW_ACCURACY"></a>
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<td class="detailHeaderName">LOW_ACCURACY</td><td class="detailHeaderType">constant</td><td class="detailHeaderRule">&nbsp;</td>
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<code>public static const LOW_ACCURACY:String = "lowAccuracy"</code>
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<td class="detailHeaderName">SHORT_PERIOD</td><td class="detailHeaderType">constant</td><td class="detailHeaderRule">&nbsp;</td>
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<code>public static const SHORT_PERIOD:String = "shortPeriod"</code>
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<center class="copyright">Author : Yongho, Ji (jidolstar@gmail.com)</center>
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